Quantum Mechanics can be understood through stochastic optimization on spacetimes.

The main contribution of this paper is to explain where the imaginary structure comes from in quantum mechanics. It is shown how the demand of relativistic invariance is key and how the geometric structure of the spacetime together with the demand of linearity are fundamental in understanding the foundations of quantum mechanics. We derive the Stueckelberg covariant wave equation from first principles via a stochastic control scheme. From the Stueckelberg wave equation a Telegrapher's equation is deduced, from which the classical relativistic and nonrelativistic equations of quantum mechanics can be derived in a straightforward manner. We therefore provide meaningful insight into quantum mechanics by deriving the concepts from a coordinate invariant stochastic optimization problem, instead of just stating postulates.

Ultrasound Arthroscopy of Hip in Treatment of Osteochondritis Dissecans.

An ultrasound arthroscopy (UA) technique is a promising tool for the evaluation of the articular cartilage during arthroscopic examination. However, the applicability of UA for the evaluation of the hip joint is unknown. We describe a UA assessment of a patient with osteochondritis dissecans at the femoral head. An ultrasound catheter designed for intravascular imaging was inserted into the hip joint by use of conventional arthroscopic portals, and the cartilage surfaces of the femoral head and acetabulum were investigated with ultrasound. UA provided essential quantitative information on the integrity of the articular cartilage and the condition of the subchondral plate not assessable with conventional arthroscopy. Furthermore, the UA technique provided the possibility to monitor arthroscopy-assisted retrograde drilling and bone transplantation in the hip joint.

Finite difference time domain model of ultrasound propagation in agarose scaffold containing collagen or chondrocytes.

Measurement of ultrasound backscattering is a promising diagnostic technique for arthroscopic evaluation of articular cartilage. However, contribution of collagen and chondrocytes on ultrasound backscattering and speed of sound in cartilage is not fully understood and is experimentally difficult to study. Agarose hydrogels have been used in tissue engineering applications of cartilage. Therefore, the aim of this study was to simulate the propagation of high frequency ultrasound (40 MHz) in agarose scaffolds with varying concentrations of chondrocytes (1 to 32 × 10(6) cells/ml) and collagen (1.56-200 mg/ml) using transversely isotropic two-dimensional finite difference time domain method (FDTD). Backscatter and speed of sound were evaluated from the simulated pulse-echo and through transmission measurements, respectively. Ultrasound backscatter increased with increasing collagen and chondrocyte concentrations. Furthermore, speed of sound increased with increasing collagen concentration. However, this was not observed with increasing chondrocyte concentrations. The present study suggests that the FDTD method may have some applicability in simulations of ultrasound scattering and propagation in constructs containing collagen and chondrocytes. Findings of this study indicate the significant role of collagen and chondrocytes as ultrasound scatterers and can aid in development of modeling approaches for understanding how cartilage architecture affects to the propagation of high frequency ultrasound.

Phased-array ultrasound technology enhances accuracy of dual frequency ultrasound measurements - towards improved ultrasound bone diagnostics.

Overlying soft tissues attenuate ultrasound backscattered from bone, complicating diagnostics of osteoporosis at the most important fracture sites. Dual-frequency ultrasound technique (DFUS) has been proposed to solve this problem through determination of thickness and composition of overlying soft tissue. This study applies DFUS technique for the first time with a phased-array transducer to investigate if the thickness of two interfering layers (oil and water) can be accurately determined in a variety of configurations. Results indicate that DFUS may be used with phased-array ultrasound systems, making them a suitable combination to consider in future development of clinical in vivo ultrasound methodologies.

Species-Independent Modeling of High-Frequency Ultrasound Backscatter in Hyaline Cartilage.

Apparent integrated backscatter (AIB) is a common ultrasound parameter used to assess cartilage matrix degeneration. However, the specific contributions of chondrocytes, proteoglycan and collagen to AIB remain unknown. To reveal these relationships, this work examined biopsies and cross sections of human, ovine and bovine cartilage with 40-MHz ultrasound biomicroscopy. Site-matched estimates of collagen concentration, proteoglycan concentration, collagen orientation and cell number density were employed in quasi-least-squares linear regression analyses to model AIB. A positive correlation (R(2) = 0.51, p < 10(-4)) between AIB and a combination model of cell number density and collagen concentration was obtained for collagen orientations approximately perpendicular (>70°) to the sound beam direction. These findings indicate causal relationships between AIB and cartilage structural parameters and could aid in more sophisticated future interpretations of ultrasound backscatter.

Diagnosis of Knee Osteochondral Lesions With Ultrasound Imaging.

Evaluation of articular cartilage and subchondral bone is essential in the diagnosis of joint diseases and injuries. Interobserver and intraobserver reproducibilities of arthroscopic grading are only poor to moderate. Thus, for quantitative and objective evaluation of cartilage and subchondral bone, ultrasound arthroscopy (UA) has been introduced to clarify this dilemma. Assessment of the clinical feasibility of high-frequency ultrasonography (US) during 6 knee arthroscopies was conducted, and the surgical technique is presented. US imaging was conducted with a flexible 9-MHz US catheter inserted into the joint through conventional portals. US and arthroscopy videos were synchronously recorded, and US parameters for cartilage and subchondral bone characteristics were measured. Arthroscopy and US imaging were combined to perform cartilage grading. UA produced quantitative data on lesion size, as well as cartilage quality, and showed subchondral bone changes. Visualization of an osteochondritis dissecans lesion not detected by conventional arthroscopy and US-guided retrograde drilling were possible with UA. To conclude, UA proved to be clinically feasible and aided in the diagnosis when assessing knee osteochondral lesions.

Ultrasound Backscattering Is Anisotropic in Bovine Articular Cartilage.

Collagen, proteoglycans and chondrocytes can contribute to ultrasound scattering in articular cartilage. However, anisotropy of ultrasound scattering in cartilage is not fully characterized. We investigate this using a clinical intravascular ultrasound device with ultrasound frequencies of 9 and 40 MHz. Osteochondral samples were obtained from intact bovine patellas, and cartilage was imaged in two perpendicular directions: through articular and lateral surfaces. At both frequencies, ultrasound backscattering was higher (p < 0.05) when measured through the lateral surface of cartilage. In addition, the composition and structure of articular cartilage were investigated with multiple reference methods involving light microscopy, digital densitometry, polarized light microscopy and Fourier infrared imaging. Reference methods indicated that acoustic anisotropy of ultrasound scattering arises mainly from non-uniform distribution of chondrocytes and anisotropic orientation of collagen fibers. To conclude, ultrasound backscattering in articular cartilage was found to be anisotropic and dependent on the frequency in use.

Inter-individual changes in cortical bone three-dimensional microstructure and elastic coefficient have opposite effects on radial sound speed.

Knowledge about simultaneous contributions of tissue microstructure and elastic properties on ultrasound speed in cortical bone is limited. In a previous study, porosities and elastic coefficients of cortical bone in human femurs were shown to change with age. In the present study, influences of inter-individual and site-dependent variation in cortical bone microstructure and elastic properties on radial speed of sound (SOS; at 4, 6, and 8 MHz) were investigated using three-dimensional (3D) finite difference time domain modeling. Models with fixed (nominal model) and sample-specific (sample-specific model) values of radial elastic coefficients were compared. Elastic coefficients and microstructure for samples (n = 24) of human femoral shafts (n = 6) were derived using scanning acoustic microscopy and micro-computed tomography images, respectively. Porosity-related SOS varied more extensively in nominal models than in sample-specific models. Linear correlation between pore separation and SOS was similar (R = 0.8, p < 0.01, for 4 MHz) for both models. The determination coefficient (R(2)= 0.75, p < 0.05) between porosity and radial SOS, especially at 4 MHz, was highest in the posterior quadrant. The determination coefficient was lower for models with sample-specific values of radial elastic coefficient implemented (R(2) < 0.33, p < 0.05), than for nominal models (0.48 < R(2)< 0.63, p < 0.05). This information could be useful in in vivo pulse-echo cortical thickness measurements applying constant SOS.

Ultrasound arthroscopy of human knee cartilage and subchondral bone in vivo.

Arthroscopic ultrasound imaging enables quantitative evaluation of articular cartilage. However, the potential of this technique for evaluation of subchondral bone has not been investigated in vivo. In this study, we address this issue in clinical arthroscopy of the human knee (n = 11) by determining quantitative ultrasound (9 MHz) reflection and backscattering parameters for cartilage and subchondral bone. Furthermore, in each knee, seven anatomical sites were graded using the International Cartilage Repair Society (ICRS) system based on (i) conventional arthroscopy and (ii) ultrasound images acquired in arthroscopy with a miniature transducer. Ultrasound enabled visualization of articular cartilage and subchondral bone. ICRS grades based on ultrasound images were higher (p < 0.05) than those based on conventional arthroscopy. The higher ultrasound-based ICRS grades were expected as ultrasound reveals additional information on, for example, the relative depth of the lesion. In line with previous literature, ultrasound reflection and scattering in cartilage varied significantly (p < 0.05) along the ICRS scale. However, no significant correlation between ultrasound parameters and structure or density of subchondral bone could be demonstrated. To conclude, arthroscopic ultrasound imaging had a significant effect on clinical grading of cartilage, and it was found to provide quantitative information on cartilage. The lack of correlation between the ultrasound parameters and bone properties may be related to lesser bone change or excessive attenuation in overlying cartilage and insufficient power of the applied miniature transducer.

Application of optical coherence tomography enhances reproducibility of arthroscopic evaluation of equine joints.

BACKGROUND: Arthroscopy is widely used in various equine joints for diagnostic and surgical purposes. However, accuracy of defining the extent of cartilage lesions and reproducibility in grading of lesions are not optimal. Therefore, there is a need for new, more quantitative arthroscopic methods. Arthroscopic optical coherence tomography (OCT) imaging is a promising tool introduced for quantitative detection of cartilage degeneration and scoring of the severity of chondral lesions. The aim of this study was to evaluate the inter-investigator agreement and inter-method agreement in grading cartilage lesions by means of conventional arthroscopy and with OCT technique. For this aim, 41 cartilage lesions based on findings in conventional and OCT arthroscopy in 14 equine joints were imaged, blind coded and independently ICRS (International Cartilage Repair Society) scored by three surgeons and one PhD-student. RESULTS: The intra- and inter-investigator percentages of agreement by means of OCT (68.9% and 43.9%, respectively) were higher than those based on conventional arthroscopic imaging (56.7% and 31.7%, respectively). The intra-investigator Kappa coefficients were 0.709 and 0.565 for OCT and arthroscopy, respectively. Inter-investigator Kappa coefficients were 0.538 and 0.408 for OCT and arthroscopy, respectively. CONCLUSIONS: OCT can enhance reproducibility of arthroscopic evaluation of equine joints.

2-D finite difference time domain model of ultrasound reflection from normal and osteoarthritic human articular cartilage surface.

Quantitative high-frequency ultrasonic evaluation of articular cartilage has shown a potential for the diagnosis of osteoarthritis, where the roughness of the surface, collagen and proteoglycan contents, and the density and mechanical properties of cartilage change concurrently. Experimentally, these factors are difficult to investigate individually and thus a numerical model is needed. The present study is the first one to use finite difference time domain modeling of pulse-echo measurements of articular cartilage. Ultrasound reflection from the surface was investigated with varying surface roughness, material parameters (Young's modulus, density, longitudinal, and transversal velocities) and inclination of the samples. The 2-D simulation results were compared with the results from experimental measurements of the same samples in an identical geometry. Both the roughness and the material parameters contributed significantly to the ultrasound reflection. The angular dependence of the ultrasound reflection was strong for a smooth cartilage surface but disappeared for the samples with a rougher surface. These results support the findings of previous experimental studies and indicate that ultrasound detects changes in the cartilage that are characteristic of osteoarthritis. In the present study there are differences between the results of the simulations and the experimental measurements. However, the systematic patterns in the experimental behavior are correctly reproduced by the model. In the future, our goal is to develop more realistic acoustic models incorporating inhomogeneity and anisotropy of the cartilage.